1. Field of the invention
The invention relates generally to a delta-sigma fractional type divider, and more particularly to, a structure of a delta-sigma fractional type divider which is simple, has a wide-band frequency mixing capability and can obtain a delta-sigma mode by maximum.
2. Description of the Prior Art
A frequency synthesizer is a circuit for obtaining necessary frequencies depending on a digital code value. The frequency synthesizer is mainly divided into an integer type frequency synthesizer for producing an output frequency of an integer times using an input frequency of a frequency-phase detector, and a fractional type frequency synthesizer improved in phase, synchronizing time, etc. compared to the integer type frequency synthesizer.
The fractional type frequency synthesizer has a high spur in process of being implemented even though it's various advantages. Thus, the fractional type frequency synthesizer has a current compensation structure using digital-analog converter, a phase interpolation structure, and a delta-sigma structure in order to remove the spur.
The delta-sigma structure disperses the energy of spur generated in a pulse swallowing fraction ratio N frequency synthesizer and transforms the shape of the energy (noise shaping) to implement a high performance frequency synthesizer.
[Dual Modulus Fractional N]
FIG. 1(a) is a block diagram for describing a basic fractional type divider, and FIGS. 1(b) and FIG. 1(c) are waveforms for describing the operation and variations in the difference of the phases of the divider.
The structure of the basic fractional type divider in FIG. 1(a) controls the dual modulus prescaler 1 to produce the division ratio such as below Equation 1 wherein the Tp+1 is a time section which has the 1/(P+1) division ratio and the TP is a time section which has the 1/P division ratio.                               f          vco                =                                            [                              N                +                                                      T                                          P                      +                      1                                                                                                  T                      P                                        +                                          T                                              P                        +                        1                                                                                                        ]                        ·                          f              ref                                =                                    (                              N                ·                f                            )                        ·                          f              ref                                                          [                  Equation          ⁢                                           ⁢          1                ]            
In this process, however, variations in the phase generated in period of 1(.f)*fref causes to modulate an oscillator through a charge pump and a loop filter, so that a high spur is generated at N*(.f)fref (N is a positive integer) against the output center frequency of the oscillator. This spur is difficult to remove using the loop filter. Further, the sensitivity of a communication system is decreased by the spur near the output frequency of the oscillator.
The spur can be generated by a control voltage as follows. When the output of the oscillator is Vout(t)=A(t)cos[w0t+Φ(t)], the phase noise by the frequency modulation of a control signal Vc(t) can be expressed as follows:Vout(t)=A·cos[(ω0+KVC0·VC(t))·t], VC(t)=Am·sin(ωout) ω=ω0+KVCO·VC(t),       ϕ    0    =            ∫                        (                                    ω              0                        +                                          K                VCO                            ·                                                V                  c                                ⁡                                  (                  t                  )                                                              )                ⁢                  ⅆ          t                      =                            ω          0                ⁢        t            +                        K          VCO                ⁢                              ∫                          -              ∞                        t                    ⁢                                                    V                c                            ⁡                              (                t                )                                      ⁢                                                   ⁢                          ⅆ              t                                          Therefore, Vout(t) can be approximated as                     V        out            ⁡              (        t        )              ≈                  A        ⁢                                   ⁢        cos        ⁢                                   ⁢                  w          0                ⁢        t            -                                    A            m                    ·          A          ·                                    K              VCO                                      ω              m                                ·          sin                ⁢                                   ⁢                  ω          0                ⁢                  t          ·          sin                ⁢                                   ⁢                  ω          m                ⁢        t              ⁢          ⁢           =            A      ⁢                           ⁢      cos      ⁢                           ⁢              ω        0            ⁢      t        -                                        A            m                    ⁢          A          ⁢                                           ⁢                      K            VCO                                    2          ⁢                      ω            m                              ⁢              {                                            cos              ⁡                              (                                                      ω                    0                                    -                                      ω                    m                                                  )                                      ⁢            t                    +                                    cos              ⁡                              (                                                      ω                    0                                    +                                      ω                    m                                                  )                                      ⁢            t                          }            
Therefore, spur is generated at to ω0±ωm.
[Multi-Modulus Fractional N]
The dual modulus fractional ratio N can be implemented into a first order delta-sigma. As the dual modulus fractional ratio N has the quantization level of /P and /(P+1) by one bit control, at this time, the energy of spur can be effectively dispersed and reduced. In general, the dual modulus fractional ratio N is implemented into a delta sigma of over third order. In case of designing the dual modulus fractional ratio N having a delta sigma of over third order, a delta-sigma modulator of a mash type that can obtain an effect of transformation of energy shape and can obtain high stability is usually applied to a frequency synthesizer. As an output of the modulator of a mash type is multi-bit, a multi-modulus prescaler is required in order for the dividing circuit to accept it. As a result, the dividing circuit requires complicated dividing unit and control unit.
A process of inducing the mash type structure is first described, and problems in the conventional multi-modulus dividing circuit is then described.
At first, over-sampling (quantization) is described. If quantization errors are white noise, the mean square value is:       ⅇ    rms    2    =                    1        Δ            ⁢                        ∫                                    -              Δ                        /            2                                              +              Δ                        /            2                          ⁢                              ⅇ            2                    ⁢                                           ⁢                      ⅆ            ⅇ                                =                  Δ        2            12      
And if the quantized signal is sampled to fS=1/t, the spectral density of a band is:       E    ⁡          (      f      )        =                              ⅇ          rms                ⁡                  (                      2                          f              s                                )                            1        /        2              =                  ⅇ        rms            ⁢                        2          ⁢          τ                    
Noise power of a signal band 0≦f≦f0 is       n    0    2    =                    ∫        0                  f          0                    ⁢                                    ⅇ            2                    ⁡                      (            f            )                          ⁢                  ⅆ          f                      =                            ⅇ          rms          2                ⁡                  (                      2            ⁢                          f              0                        ⁢            τ                    )                    =                        ⅇ          rms          2                          O          ⁢                                           ⁢          S          ⁢                                           ⁢          R                    , whereOSR=fs/2f0=1/2f0t. 
From the above results, it could be seen that over-sampling reduces the in-bands rms quantization noise(n0) to a square root of OSR. Further, it could be seen that the in-band noise is reduced by about 3 dB (corresponding to ½ bit resolution) when the sampling frequency is doubled.
Referring now to FIGS. 2a˜FIG. 2c, first order delta-sigma modulation will be described. It was found that quantization using a simple over-sampling and filtering could improve SNR of 3 dB when the sampling frequency is made twice, while the in-band noise of a signal could be more reduced if feedback is introduced to the process.
FIGS. 2a˜FIG. 2c are block diagrams of the first order delta-sigma modulator. FIG. 1a illustrates a first order delta-sigma modulator, FIG. 2b illustrates an equivalent model of sampled data and FIG. 2c illustrates a Z-domain model. Analysis for the first order delta-sigma can be :expressed as follows:S(I)=x(I)=y(I), w(I+1)=s(I)+w(I), y(I)=w(I)30 c(I) y(I)=x(I)=s(I)=x(I)−[w(I+1)−w(I)]w(I)+e(I)=x(I)−w(I+1)+w(I) w(I+1)=x(I)−e(I)=y(I+1)−e(I+1) y(I)=x(I−1)+e(I)−(I−1) 
Therefore,y(I)=xi-1+(ei−ei-1). 
In other words, the delta-sigma shown in FIG. 2 causes to time-delay an original signal so that the original signal can be maintained intact, and reduce quantization errors by differentiation.
In order to obtain the spectral density of ni=(ei−ei-1), i.e., a noise due to modulation, Z-transform is performed. Thus, as N(z)=(1−z−1)E(z) and z=ejωL (L is sampling frequency),       N    ⁡          (      f      )        =                    E        ⁡                  (          f          )                    ⁢                                1          -                      ⅇ                                          -                jω                            ⁢                                                           ⁢              τ                                                    =          2      ⁢              ⅇ        rms            ⁢                        2          ⁢          τ                    ⁢              sin        ⁡                  (                      ωτ            2                    )                    
Therefore, it could be seen that the noise component of a low frequency can be reduced.
The noise power at the signal band is:             n      0      2        =                            ∫          0                      f            0                          ⁢                                                                          N                ⁡                                  (                  f                  )                                                                    2                    ⁢                                           ⁢                      ⅆ            f                              ≈                        ⅇ          rms          2                ⁢                              π            2                    3                ⁢                              (                          2              ⁢                              f                0                            ⁢              τ                        )                    3                      ,            f      s      2        ⪢          f      0      2      
Also, the rms value is:       n    0    =                    ⅇ        rms            ⁢              π                  3                    ⁢                        (                      2            ⁢                          f              0                        ⁢            τ                    )                          3          /          2                      =                  ⅇ        rms            ⁢              π                  3                    ⁢                        (                      O            ⁢                                                   ⁢            S            ⁢                                                   ⁢            R                    )                                      -            3                    /          2                    
Thus, it could be seen that a noise is reduced by about 9 dB (corresponding to 1.5 bit resolution) if the over-sampling ratio is doubled. If the input of the delta sigma is a direct current (DC), repetitive noise patterns appear, which is called a patterned noise. And the above equation can be easily obtained through a closed-loop transfer function of a Z-domain model shown in FIG. 2(c).                               Y          ⁡                      (            z            )                          =                                                            1                /                                  (                                      1                    -                                          z                                              -                        1                                                                              )                                                            1                +                                                      z                                          -                      1                                                        /                                      (                                          1                      -                                              z                                                  -                          1                                                                                      )                                                                        ·                          X              ⁡                              (                z                )                                              +                                    1                              1                +                                                      z                                          -                      1                                                        /                                      (                                          1                      -                                              z                                                  -                          1                                                                                      )                                                                        ·                          E              ⁡                              (                z                )                                                                            =                              X            ⁡                          (              z              )                                +                                    (                              1                -                                  z                                      -                    1                                                              )                        ·                          E              ⁡                              (                z                )                                                        
The delta sigma performs a noise shaping by which the energy of modulation noise is pushed out to the signal band by a feedback using the integrator. At this time, the characteristic of the integrator determines the shape of the noise spectrum.
Generally, in case that a L-order loop is formed and system is stable, the spectral density is:                 N      ⁡              (        f        )                  ⁢      ⅇ    rms    ⁢            2      ⁢      τ        ⁢            (              2        ⁢                  sin          ⁡                      (                          ωτ              2                        )                              )        L  
In case of OSR>2, the rms noise at the signal band is:
FIG. 3 illustrates a third order delta-sigma (L=3). The rms noise of the                     n        0            =                        ⅇ          rms                ⁢                              π            L                                                              2                ⁢                L                            +              1                                      ⁢                              (                          O              ⁢                                                           ⁢              S              ⁢                                                           ⁢              R                        )                                -                          (                              L                +                                  1                  2                                            )                                            ,                  O        ⁢                                   ⁢        S        ⁢                                   ⁢        R            =                        1          /          2                ⁢                  f          0                ⁢        τ                                n        0            =                        ⅇ          rms                ⁢                              π            L                                                              2                ⁢                L                            +              1                                      ⁢                              (                          O              ⁢                                                           ⁢              S              ⁢                                                           ⁢              R                        )                                -                          (                              L                +                                  1                  2                                            )                                            ,                  O        ⁢                                   ⁢        S        ⁢                                   ⁢        R            =                        1          /          2                ⁢                  f          0                ⁢        τ            third order delta-sigma is expressed as
The delta-sigma modulator of this high order can further reduce the quantization noise of a signal band while the delta-sigma structure shown in FIG. 3 has a problem in the stability since it is a control system of a high order constituting a multi-loop. For example, the first and second order delta-sigma modulator has loop gains of 2.0 and 1.33. However, the third order delta-sigma modulator is unstable even having the loop gain of 1.15. The modulator in FIG. 3 has one bit output of +1 and −1, and also has the division ratio at the time region expressed as             f      REF        =                  f        VCO                    N        +                  b          ⁡                      (            t            )                                ,wherein b(t) is a bit stream of the modulator controlling the dual modulus prescaler. Therefore, assuming that the fractional value (DC) to be obtained is K/M and the quantization noise is q(t),       f    REF    =            f      VCO              N      +              K        M            +              q        ⁡                  (          t          )                    
At this time, K is a constant of the modulator input and M is the modulus of the modulator adder.
Now, mash type delta-sigma modulator will be described.
The mash structure where a stable first order delta-sigma structure is cascaded has a high-order noise-shaping characteristic and also allows an stable structure to be implemented.
FIG. 4 illustrates the mash type modulator in a Z-domain. At this time, the noise transfer function can be obtained by the following equation.Y1(z)=(1−z−1)E1(z)+X(z) Y2(z)=−E1(z)+(1−z−1)E2(z) Y2′(z)=−(1−z−1)E1(z)+(1−z−1)2E2(z) Y3(z)=−E2(z)+(1−Z−1)E3(z) Y3′(z)=−(1−z−1)E2(z)+(1−z−1)3E3(z) Therefore,Y(z)=X(z)+(1−z−1)3E3(z) where the delta-sigma input X(z) is a fractional value of the PLL frequency synthesizer. If the division number of a prescaler is P, N(z)=P(z)+Y(z)=P(z)+X(z)+(1+z−1)3E3(z) can be obtained. From the above result, it could be seen that the mash type modulator used in the present invention has noise-shaping characteristics.
Most of conventional frequency synthesizers requires a multi-modulus dividing circuit since it uses a mash type modulator having a multi-bit output so that the above stability and a noise shaping effect of a high order can be satisfied.
FIG. 5 illustrates multi-modulus dividing circuit using a conventional direct-convertible counter. The multi-modulus dividing circuit includes a control unit 11 for receiving control signals D0, D1, and a phase selector 13 for producing /4/5/6/7 using the control signals. At this time, D2, D3, D4 and D5 control the division ratio depending on respective code values. The multi-modulus dividing circuit can be implemented in various structure as well as the structure shown in FIG. 5. The multi-modulus division structure, however, requires several dividing circuits 12 such as 2/3, and the like. Further, as control of those dividing circuits must be performed by each of dividing stages. Thus, the multi-modulus division structure has disadvantages that it is complicated and is difficult to be designed.